how the winner calculated when the time ends

 There are two clocks, one for each player. A player's clock does not count down unless it is that player's turn to move. The player whose clock reaches 0 loses at that moment.

An exception is if a player runs out of time, and the opponent only as their king. Then the game ends in a draw.

Close - the person whose clock runs out of time first will lose unless his opponent does not have enough material to win, in which case it is a draw: clearly if your opponent only has a king, it would be a draw, but it would also be a draw if they had, say, just a king and a knight.

If the opponent has a single pawn, they will win - if you're very short on time but well ahead on material, it's generally worthwhile sacrificing pieces to eat up the remaining pawns so that when you run out of time, it will still be a draw for you rather than a loss.

Well, I don't know the specifics. I realize there's more to it, and appreciate the detail, but at least to me it gets a little confusing.

For example does running out of time vs an opponent who has two knights and a king result in a draw on chess.com? It is enough material to mate (but not enough to force a mate in most positions).